On the general form of bimonotone operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912184315936768 |
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| author | Hadjisavvas, Nicolas |
| author_facet | Hadjisavvas, Nicolas |
| contents | In a recent paper (2024) Camacho, Cánovas, Mart\'ınez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility problems, especially in the case the operator is also paramonotone. In the present paper we drop paramonotonicity and examine the question of finding the most general form of a bimonotone operator in a Banach space. We show that any such operator can be reduced in some sense to a single-valued, skew symmetric linear operator. This facilitates the proof of some results involving these operators in applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06517 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the general form of bimonotone operators Hadjisavvas, Nicolas Functional Analysis Optimization and Control 90C48 (Primary) 47H04 47H05 (Secondary) In a recent paper (2024) Camacho, Cánovas, Mart\'ınez-Legaz and Parra introduced bimonotone operators, i.e., operators $T$ such that both $T$ and $-T$ are monotone, and found some interesting applications to convex feasibility problems, especially in the case the operator is also paramonotone. In the present paper we drop paramonotonicity and examine the question of finding the most general form of a bimonotone operator in a Banach space. We show that any such operator can be reduced in some sense to a single-valued, skew symmetric linear operator. This facilitates the proof of some results involving these operators in applications. |
| title | On the general form of bimonotone operators |
| topic | Functional Analysis Optimization and Control 90C48 (Primary) 47H04 47H05 (Secondary) |
| url | https://arxiv.org/abs/2501.06517 |